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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=17/4, b>=a > For fixed z and a=17/4, b=17/4





http://functions.wolfram.com/07.23.03.an2d.01









  


  








Input Form





Hypergeometric2F1[17/4, 17/4, 1/2, z] == (1/(7605 Pi^(3/2))) ((-((128 Sqrt[z] (2025 + 13245 z + 11979 z^2 + 1423 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^8) + (128 Sqrt[z] (2025 + 13245 z + 11979 z^2 + 1423 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^8 + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((7605 + 121995 Sqrt[z] + 155745 z + 691935 z^(3/2) + 249375 z^2 + 517281 z^(5/2) + 46027 z^3 + 45045 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((-7605 + 121995 Sqrt[z] - 155745 z + 691935 z^(3/2) - 249375 z^2 + 517281 z^(5/2) - 46027 z^3 + 45045 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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<ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 155745 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 121995 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -7605 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02